Gravity in equator v/s pole of Neutron Star

GRAVITY IN EQUATOR V/S POLE OF NEUTRON STAR

The Neutron Star is formed after super nova explosion when the remnant mass is 3 to 5 solar masses. Neutron star is primarily composed of neutrons and has the same density as that of an atom. They have a strong surface gravity and escape velocity which is one third the speed of light. The closest Neutron star is about 600 light years away. Gravity on the surface of Neutron Star varies due to its rotation. Since Neutron Star rotates, all points on its surface perform circular motion except the North and South Pole. The points at equator perform circular motion of maximum radii as compared to other points. The polar points do not perform circular motion but rotate about their own axis. 

Consider two points, equator and North Pole on Neutron Star’s surface. We’ll compare acceleration due to gravity (g) between these two points.

ASSUMPTIONS
The equator and pole locations are not terrain but plains

Density of Neutron Star is constant throughout

Neutron Star is a perfect homogeneous sphere

Angular velocity is constant throughout

PHYSICAL CHARACTERISTICS

Mean Radius R= 11 km

Mass M = 2*2*10³⁰ kg

Rotational velocity = 716 radian/s or 43000rpm

Density = 3.7*10¹⁷ to 5.9*10¹⁷ kg/m³

CALCULATION

Acceleration due to gravity on pole:

g = GM/R²

G – Universal Gravitation constant = 6.67*10^-11 Nm²/kg²

g = [6.67*10^-11 *2* 2*10³⁰]/ [11*1000]²

g = 2.2049*10¹²/(11000)²

g (φ) = 2.2049*10¹² m/s²

φ – Latitude = 90⁰ for poles

Acceleration due to gravity on equator:

We can find acceleration due to gravity on equator by using the formula,

g’(φ) = g(φ) – Rω²cos²φ

φ - Latitude = 0⁰ for equator

g’(φ) = 2.2049*10¹² – 11,000*(716)²

g’(φ) = 2.2049*10¹² – 5639216000

g’(φ) = 2.1992*10¹² m/s²

CONCLUSION

On comparing g (φ) and g’ (φ) we observe that gravity at pole is just slightly greater than that at the equator. This is because the Neutron Star has a very strong gravitational force and even the extreme angular velocity is not enough to cause a significant reduction in the acceleration due to gravity.

The difference is g (φ) - g’ (φ) = 2.2049*10¹² – 2.1992*10¹² = 5639216000 m/s²